A fast algorithm for computing minimum cross-entropy positive time-frequency distributions

An algorithm for obtaining nonnegative, joint time-frequency distributions Q(t, f) satisfying the univariate marginals \s(t)\(2) and \S(f)\(2) is presented and applied. The advantage of the algorithm presented is that large time series records can be processed without requirements for large random access memory (RAM) and central processing unit (CPU) time. This algorithm is based on the Loughlin ct al. method for synthesizing positive distributions using the principle of minimum cross entropy. The nonnegative distributions with the correct marginals that are obtained using this approach are density functions as proposed by Cohen and Zaparovanny and Cohen and Posch. Three examples are presented: The first is a nonlinear frequency modulation (FM) sweep signal (simulated data); the second and third are of physical systems (real data). The second example is the signal for the acoustic scattering response of an elastic cylindrical shell structure. The third example is of an acoustic transient signal from an underwater vehicle. Example one contains 7500 data points, example two contains 256 data points, and example three contains in excess of 30 000 data points. The RAM requirements using the original Loughlin et al. algorithm for a 7500 data point signal is 240 mega bytes and for a 30 000 data point signal is 3.5 billion bytes. The new algorithm reduces the 240 mega byte requirement to 1 mega byte and the 3.5 billion byte requirement to 4 million bytes. Furthermore, the fast algorithm runs 240 times faster for the 7500 data point signal and 3000 times faster for the 30 000 data point signal as compared with the original Loughlin ct al. algorithm.